It is well known that the topological surface states (TSSs) of a topological insulator (TI) are protected by the time-reversal symmetry (TRS). Systems with broken TRS, however, can still host the TSSs if they remain invariant under the combined symmetry operation S = ΘT_1/2, where Θ is the TRS operator and T_1/2 is the translation operation along a crystal axisby half of the corresponding lattic constant [1]. Here, for the first time, we demonstrate that the pressurized SmB₆ can possibly be classified into the antiferromagnetic topological systems (AFTSs). In addition to propose the possible candidacy for being an AFTS, in this work we also illustrate the anomalous TSSs in an AFTS which is not discussed in the original work. Originating from the interplay between the topological properties and the antiferromagnetic surface magnetization, the topological surface states of the AFT phase behave differently as compared with those of a topological insulator. Besides, the AFT insulators are also found promising in the generation of tunable spin currents, which is an important application in spintronics.

[1] Roger S. K. Mong, Andrew M. Essin, and Joel E. Moore, Phys. Rev. B 81, 245209 (2010).